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Mathematics Education Research Journal

, Volume 27, Issue 4, pp 637–662 | Cite as

Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks

  • Ariyadi WijayaEmail author
  • Marja van den Heuvel-Panhuizen
  • Michiel Doorman
Original Article

Abstract

In this study, we investigated teachers’ teaching practices and their underlying beliefs regarding context-based tasks to find a possible explanation for students’ difficulties with these tasks. The research started by surveying 27 Junior High School teachers from seven schools in Indonesia through a written questionnaire. Then, to further examine teachers’ teaching practices related to context-based tasks, four teachers were observed and video recorded in two mathematics lessons in which they were asked to deal with context-based tasks. The questionnaire data revealed that the teachers had a tendency toward a view on teaching and learning mathematics which includes encouraging students to be actively involved in solving problems in various contexts. Although this finding suggests that the teachers may offer opportunities to learn context-based tasks to students, the questionnaire data also revealed that the teachers saw context-based tasks as plain word problems. Furthermore, the observations disclosed that their teaching was mainly teacher-centered and directive, which is not considered to be supportive for learning to solve context-based tasks. Combining the findings of this study with the results from our earlier study on Indonesian students’ errors when solving context-based tasks, we found a relationship between how Indonesian teachers teach context-based tasks and the errors Indonesian students make in solving these tasks. These findings support the conclusion that insufficient opportunity-to-learn to solve context-based tasks offered by teachers is a possible explanation for students’ difficulties in solving these tasks.

Keywords

Context-based tasks Students’ difficulties Teachers’ beliefs Teachers’ teaching practices 

Notes

Acknowledgments

This research was supported by the Indonesian Ministry of Education and Culture under the project of Better Education through Reformed Management and Universal Teacher Upgrading (BERMUTU) IDA CREDIT NO.4349-IND, LOAN NO.7476-IND.

References

  1. Adamson, S., Burtch, M., Cox, T., Banks, D., Judson, E., & Lawson, T. (2002). Nature of mathematics survey. Paper presented at the 28th AMATYC Annual Conference, Phoenix, Arizona, USA,November 14–17, 2002.Google Scholar
  2. Antonius, S., Haines, C., Jensen, T. H., Niss, M., & Burkhardt, H. (2007). Classroom activities and the teacher. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 295–308). New York: Springer.CrossRefGoogle Scholar
  3. Barnes, M. (2000). ‘Magical’ moments in mathematics: insights into the process of coming to know. For the Learning of Mathematics, 20(1), 33–43.Google Scholar
  4. Bell, C. V., & Pape, S. J. (2012). Scaffolding students’ opportunities to learn mathematics through social interactions. Mathematics Education Research Journal, 24(4), 423–445.CrossRefGoogle Scholar
  5. Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68.CrossRefGoogle Scholar
  6. Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. B. Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). New York: Springer.CrossRefGoogle Scholar
  7. Blum, W., & Ferri, R. B. (2009). Mathematical modelling: can it be taught and learnt? Journal of Mathematical Modelling and Application, 1(1), 45–58.Google Scholar
  8. Blum, W., & Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? The example “Sugarloaf”. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): education, engineering and economics (pp. 222–231). Chichester: Horwood Publishing.CrossRefGoogle Scholar
  9. Brewer, D. J., & Stasz, C. (1996). Enhancing opportunity to learn measures in NCES data. In G. Hoachlander, J. E. Griffith, & J. H. Ralph (Eds.), From data to information: new directions for the National Center for Education Statistics (pp. 3.1–3.28). Washington: U.S. Department of Education.Google Scholar
  10. Chapman, O. (2009). Teachers’ conceptions and use of mathematical contextual problems in Canada. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds. Modelling verbal descriptions of situations (pp. 227–244). Rotterdam: Sense Publishers.Google Scholar
  11. Clements, M. A. (1980). Analyzing children’s errors on written mathematical task. Educational Studies in Mathematics, 11(1), 1–21.CrossRefGoogle Scholar
  12. Cooper, B., & Dunne, M. (2000). Assessing children’s mathematical knowledge: social class, sex and problem-solving. Buckingham: Open University Press.Google Scholar
  13. Council, N. R. (2001). Adding it up: helping children learn mathematics. Washington: National Academy Press.Google Scholar
  14. Erickson, F. (2006). Definition and analysis of data from videotape: some research procedures and their rationales. In J. L. Green, G. Camili, & P. B. Ellmore (Eds.), Handbook of complementary methods in education research (pp. 177–192). Mahwah: Lawrence Erlbaum.Google Scholar
  15. Ernest, P. (1989). The impacts of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics Teaching: the state of the art (pp. 249–253). New York: Falmer.Google Scholar
  16. Eurydice. (2011). Mathematics education in Europe: common challenges and national policies. Brussels: Education, Audiovisual and Culture Executive Agency.Google Scholar
  17. Forman, S. L., & Steen, L. A. (2001). Why math? Applications in science, engineering, and technological programs. Research Brief, American Association of Community Colleges.Google Scholar
  18. Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM The International Journal on Mathematics Education, 38(2), 143–162.CrossRefGoogle Scholar
  19. Gellert, U., & Jablonka, E. (2009). “I am not talking about reality”: word problems and the intricacies of producing legitimate text. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds. Modelling verbal descriptions of situations (pp. 39–53). Rotterdam: Sense Publishers.Google Scholar
  20. Graumann, G. (2011). Mathematics for problem in the everyday world. In J. Maasz & J. O’Donoghue (Eds.), Real-world problems for secondary school mathematics students: case studies (pp. 113–122). Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  21. Grouws, D. A., & Cebulla, K. J. (2000). Improving student achievement in mathematics. Brussels: International Academy of Education.Google Scholar
  22. Hagaman, J. L., Casey, K. J., & Reid, R. (2012). The effects of the paraphrasing strategy on the reading comprehension of young students. Remedial and Special Education, 33(2), 110–123.CrossRefGoogle Scholar
  23. Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte: Information Age Publishing.Google Scholar
  24. Human Development Department East Asia and Pacific Region. (2010). Inside Indonesia’s mathematics classrooms: a TIMSS Video Study of teaching and practices and student achievement. Jakarta: The World Bank.Google Scholar
  25. Husén, T. (Ed.). (1967). International study of achievement in mathematics: a comparison of twelve countries (Vol. II). New York: Wiley.Google Scholar
  26. Karbalei, A., & Amoli, F. A. (2011). The effect of paraphrasing strategy training on the reading comprehension of college students at the undergraduate level. Asian EFL Journal, 13(3), 229–344.Google Scholar
  27. Kletzien, S. B. (2009). Paraphrasing: an effective comprehension strategy. The Reading Teacher, 63(1), 73–77.CrossRefGoogle Scholar
  28. Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The effects of metacognitive instruction on solving mathematical authentic tasks. Educational Studies in Mathematics, 49(2), 225–250.CrossRefGoogle Scholar
  29. Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159–174.CrossRefGoogle Scholar
  30. Lingefjärd, T., & Meier, S. (2010). Teachers as managers of the modelling process. Mathematics Education Research Journal, 22(2), 92–107.CrossRefGoogle Scholar
  31. Maass, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285–311.CrossRefGoogle Scholar
  32. Maulana, R., Opdenakker, M.-C., Den Brok, P., & Bosker. (2012). Teacher-student interpersonal behavior in secondary mathematics classes in Indonesia. International Journal of Science and Mathematics Education, 10(1), 21–47.CrossRefGoogle Scholar
  33. Mortimore, P. (2009). Alternative models for analysing and representing countries' performance in PISA. A paper commisioned by Education International Research Institute. http://eiie.org/docs/webdepot/alternativemodelsinpisa.pdf. Retrieved in June 1, 2013
  34. NCTM. (2000). Principles and Standard for School Mathematics. Reston: the NCTM.Google Scholar
  35. Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. Victorian Institute for Educational Research Bulletin, 39, 31–43.Google Scholar
  36. OECD. (2003). The PISA 2003 Assessment Framework – Mathematics, Reading, Science, and Problem Solving Knowledge and Skills. Paris: OECD.Google Scholar
  37. OECD. (2010). PISA 2009 results: What students know and can do. Student performance in reading, mathematics, and science (Vo. I). Paris: OECD.Google Scholar
  38. OECD. (2013). PISA 2012 results: What students know and can do. Student performance in mathematics, reading and science (Vol. I). Paris: OECD.Google Scholar
  39. Prakitipong, N., & Nakamura, S. (2006). Analysis of mathematics performance of grade five students in Thailand using Newman procedure. Journal of International Cooperation in Education, 9(1), 111–122.Google Scholar
  40. Pusat Kurikulum. (2003). Kurikulum 2004. Standar kompetensi mata pelajaran matematika Sekolah Menengah Pertama dan Madrasah Tsanawiyah [The Curriculum 2004. The standard competences for Junior High School mathematics]. Jakarta: Departemen Pendidikan Nasional.Google Scholar
  41. Sam, L. C., Lourdusamy, A., & Ghazali, M. (2001). Factors affecting students’ abilities to solve operational and word problems in mathematics. Journal of Science and Mathematics Education in Southeast Asia, 24(1), 84–95.Google Scholar
  42. Sepeng, P. (2013). Use of unrealistic contexts and meaning in word problem solving: a case of second language learners in Township schools. International Journal of Research in Mathematics, 1(1), 8–14.Google Scholar
  43. Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226.CrossRefGoogle Scholar
  44. Tornroos, J. (2005). Mathematics textbooks, opportunity to learn and student achievement. Studies in Educational Evaluation, 31(4), 315–327.CrossRefGoogle Scholar
  45. Treffers, A. (1987). Three Dimensions. A model of goal and theory description in mathematics instruction – The Wiskobas Project. Dordrecht: Reidel Publishing Company.Google Scholar
  46. Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: using TIMSS to investigate the translation of policy into practice through the world of textbooks. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  47. Van den Heuvel-Panhuizen, M. (2010). Reform under attack—forty years of working on better mathematics education thrown on the scrapheap? No Way! In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia. MERGA: Fremantle.Google Scholar
  48. Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 521–525). Dordrecht: Springer.Google Scholar
  49. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making Sense of Word Problems. Lisse: Swets & Zeitlinger.Google Scholar
  50. Verschaffel, L., Van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Reconceptualising word problem as exercises in mathematical modelling. Journal für Mathematik-Didaktik, 31(1), 9–29.CrossRefGoogle Scholar
  51. Wijaya, A., Van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics tasks: an analysis of students’ errors. The Mathematics Enthusiast, 11(3), 541–554.Google Scholar
  52. Wijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65.CrossRefGoogle Scholar
  53. Wilkins, J. L. M. (2008). The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11(2), 139–164.CrossRefGoogle Scholar
  54. Xin, Z., Lin, C., Zhang, L., & Yan, R. (2007). The performance of Chinese primary school students on realistic arithmetic word problems. Educational Psychology in Practice, 23(2), 145–159.CrossRefGoogle Scholar

Copyright information

© Mathematics Education Research Group of Australasia, Inc. 2015

Authors and Affiliations

  • Ariyadi Wijaya
    • 1
    • 3
    Email author
  • Marja van den Heuvel-Panhuizen
    • 1
    • 2
  • Michiel Doorman
    • 1
  1. 1.Freudenthal Institute for Science and Mathematics Education (FIsme)Utrecht University, Princetonplein 5UtrechtThe Netherlands
  2. 2.Faculty of Social and Behavioural SciencesUtrecht UniversityUtrechtThe Netherlands
  3. 3.Mathematics Education Department - FMIPAYogyakarta State University, Kampus KarangmalangYogyakartaIndonesia

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